Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x+4y &= 6 \\ 5x+5y &= 5\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $5y = -5x+5$ Divide both sides by $5$ to isolate $y$ $y = {-x + 1}$ Substitute this expression for $y$ in the first equation. $-x+4({-x + 1}) = 6$ $-x - 4x + 4 = 6$ Simplify by combining terms, then solve for $x$ $-5x + 4 = 6$ $-5x = 2$ $x = -\dfrac{2}{5}$ Substitute $-\dfrac{2}{5}$ for $x$ back into the top equation. $+ \dfrac{2}{5}+4y = 6$ $\dfrac{2}{5}+4y = 6$ $4y = \dfrac{28}{5}$ $y = \dfrac{7}{5}$ The solution is $\enspace x = -\dfrac{2}{5}, \enspace y = \dfrac{7}{5}$.